Solve for $x$ : $5x^2 - 15x + 10 = 0$
Explanation: Dividing both sides by $5$ gives: $ x^2 {-3}x + {2} = 0 $ The coefficient on the $x$ term is $-3$ and the constant term is $2$ , so we need to find two numbers that add up to $-3$ and multiply to $2$ The two numbers $-2$ and $-1$ satisfy both conditions: $ {-2} + {-1} = {-3} $ $ {-2} \times {-1} = {2} $ $(x {-2}) (x {-1}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -2) (x -1) = 0$ $x - 2 = 0$ or $x - 1 = 0$ Thus, $x = 2$ and $x = 1$ are the solutions.